Multiple choice

A jar contains a mixture of two liquids A and B in the ratio 4 : 1. When 10 litres of the mixture is replaced with liquid B, the ratio becomes 2 : 3. The volume of liquid A present in the jar earlier was

  1. 10 litres

  2. 16 litres

  3. 15 litres

  4. 20 litres
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let initial volume be 5x (4x of A, 1x of B). After removing 10 litres, 8 litres of A and 2 litres of B are removed. Adding 10 litres of B results in (4x-8) of A and (x-2+10) of B. Setting (4x-8)/(x+8) = 2/3 gives 12x-24 = 2x+16, so 10x = 40 and x=4. Initial A is 4*4 = 16 litres.

AI explanation

Let the initial total volume of the mixture be x litres, meaning liquid A is 4x/5 and liquid B is x/5. When 10 litres are removed, 4/5 of that volume (8 litres) of liquid A is taken out, leaving 4x/5 - 8 litres of liquid A. After adding 10 litres of liquid B, the new total volume of liquid A is 2/5 of the total mixture x, leading to the equation 4x/5 - 8 = 2x/5. Solving this gives x = 20, so the initial volume of liquid A was 4/5 of 20, which is 16 litres.

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